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Statistical inference on transformation models: a self-induced smoothing approach

Author

Listed:
  • Junyi Zhang
  • Zhezhen Jin
  • Yongzhao Shao
  • Zhiliang Ying

Abstract

This paper deals with a general class of transformation models that contains many important semiparametric regression models as special cases. It develops a self-induced smoothing for the maximum rank correlation estimator, resulting in simultaneous point and variance estimation. The self-induced smoothing does not require bandwidth selection, yet provides the right amount of smoothness so that the estimator is asymptotically normal with mean zero (unbiased) and variance–covariance matrix consistently estimated by the usual sandwich-type estimator. An iterative algorithm is given for the variance estimation and shown to numerically converge to a consistent limiting variance estimator. The approach is applied to a data set involving survival times of primary biliary cirrhosis patients. Simulation results are reported, showing that the new method performs well under a variety of scenarios.

Suggested Citation

  • Junyi Zhang & Zhezhen Jin & Yongzhao Shao & Zhiliang Ying, 2018. "Statistical inference on transformation models: a self-induced smoothing approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 308-331, April.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:308-331
    DOI: 10.1080/10485252.2018.1424334
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    Cited by:

    1. Yilong Zhang & Xiaoxia Han & Yongzhao Shao, 2021. "The ROC of Cox proportional hazards cure models with application in cancer studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 195-215, April.
    2. Yu, Tao & Li, Pengfei & Chen, Baojiang & Yuan, Ao & Qin, Jing, 2023. "Maximum pairwise-rank-likelihood-based inference for the semiparametric transformation model," Journal of Econometrics, Elsevier, vol. 235(2), pages 454-469.

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